Approximate Reduction from AUC Maximization to 1-norm Soft Margin Optimization

22nd International Conference, ALT 2011 : October 5-7, 2011 : Espoo, FinlandFinding linear classifiers that maximize AUC scores is important in ranking research. This is naturally formulated as a 1-norm hard/soft margin optimization problem over pn pairs of p positive and n negative instances. However, directly solving the optimization problems is impractical since the problem size (pn) is quadratically larger than the given sample size (p+n). In this paper, we give (approximate) reductions from the problems to hard/soft margin optimization problems of linear size. First, for the hard margin case, we show that the problem is reduced to a hard margin optimization problem over p+n instances in which the bias constant term is to be optimized. Then, for the soft margin case, we show that the problem is approximately reduced to a soft margin optimization problem over p+n instances for which the resulting linear classifier is guaranteed to have a certain margin over pairs

Approximate Reduction from AUC Maximization to 1-norm Soft Margin Optimization

Finding linear classifiers that maximize AUC scores is important in ranking research. This is naturally formulated as a 1-norm hard/soft margin optimization problem over pn pairs of p positive and n negative instances. However, directly solving the optimization problems is impractical since the problem size (pn) is quadratically larger than the given sample size (p+n). In this paper, we give (approximate) reductions from the problems to hard/soft margin optimization problems of linear size. First, for the hard margin case, we show that the problem is reduced to a hard margin optimization problem over p+n instances in which the bias constant term is to be optimized. Then, for the soft margin case, we show that the problem is approximately reduced to a soft margin optimization problem over p+n instances for which the resulting linear classifier is guaranteed to have a certain margin over pairs.22nd International Conference, ALT 2011 : October 5-7, 2011 : Espoo, Finlan